# AUA E-Math Test Sample Questions A en

## Transcription

AUA E-Math Test Sample Questions A en
```AUA E-Math Test
Sample Questions A
1. If a and b are positive numbers such that a + b = 7, then
A. b-1
B. 1
C. 0
D. -1
E. a
2. If
then which of the following must be true?
A. x = 6
B. x < 3
C. x > 0
D. x2 < x
E. x2 > x
3. The point (2,1) is the midpoint of a segment with endpoints at (–5,3) and (x,y). Calculate (x,y).
A. (-3,4)
B. (-7,2)
C. (7,1)
D. (9,-1)
E. (-10,3)
4. Solve for x:
A. x=12
B. x=1/3
C. x=5
D. x=0
E. x=12/7
5. Factor
A. (x - 4)(4x2-3)
B. (x - 4)(4x2-1)
C. (x - 4)(4x2+3)
D. 4x2(x - 4)+3(4-x)
E. (x2- 4)(4x-3)
6. In the figure, AB is parallel to DE, AE = 14, CE = 7, and DE = 5. What is the length of AB?
A. 8
B. 10
C. 15
D. 14
E. 16
7. For some positive real number
, the first 3 terms of a geometric progression are
. What is the numerical value of the fourth term?
A. 25
B. 36
C. 32
and
D. 100
E. 9
8. If
and
is not equal to , then all the possible values of
are
A. 0
B. 2
C. -2
D. 0 և 2
E. None of the above
9. If the radius of a sphere is doubled, the percent increase in volume is
A. 100
B. 200
C. 400
D. 700
E. 800
10. When a natural number n is divided by 9, the remainder is x. When 2n is divided by 9, the remainder
is y. Which (x, y) pair is not possible?
A. (4,8)
B. (6,3)
C. (4,0)
D. (0, 0)
E. (8, 7)
11. Given that
, what is the value of
?
A. 0
B. 1/2
C. 1
D. log5 (2)
E. log5 (5)
12. Which of the following numbers is rational?
A. The square root of 5
B. The square root of 2 divided by 2
C. The square root of 9
D. Π
E. The square root of 2
13. If
, which of the listed values best approximates
?
A. 2.8
B. 2.3
C. 2.1
D. 1.9
E. 1.6
14. If
A. y > 5
B. y < 5
C. 0 < y < 11
D. y > 11
E. y < 11
and
, which of the following represents all possible values of
?
15. The domain of the function
is
A. x ≠ 1/2
B. x ≥ 4
C. x ≠ 4
D. x < 1/2
E. x > 0
16. If the two triangles in the figure are similar, find a.
A. 12
B. 6
C. 10
D. 16
E. 14
17. In the figure, P is the center of the circle and PQ = QR. If triangle PQR has an area of
the area of the shaded region?
, what is
A. 36π – 9√3
B. 24π -9√3
C. 18π - 9√3
D. 9π - 9√3
E. 6π - 9√3
18. If
, and a and c are doubled, what happens to the value of d?
A. The Value of d remains the same.
B. The value of d is doubled.
C. The value of d is four times greater.
D. The value of d is halved.
E. The value of d is four times smaller.
19. If
1
A. 2log2(r) for any r
B. 1 - S + T
C. 1 - S - T
D. logr(2)-1
E. Zero if r=4
and
, then
20. What is the dot product of vectors
and
if
and
.
A. -1
B. 0
C. 1
D. 2
E. -2
21. Let L be a line in some plane P and let A and B be two points on L. What is the set of points of P that
are at equal distance from A and B?
A. The midpoint of the line segment AB.
B. The points on the line perpendicular to L and passing through the midpoint of line segment AB.
C. The point on line L.
D. {A, B, midpoint of AB}
E. The points along the circle centered at the midpoint of line segment AB
22. In triangle ABC, BC = 5, AC = 7, and AB = 8. What is the cosine of angle C?
A. 1/7
B. 1/2
C. √3/2
D. 5/7
E. 8/7
23. The solution set of
A.
A. {40}
B.
B. {-40}
C.
C. {88}
is
D.
D. {-74, 74}
E.
The empty set
F.
24. If m and n are both squares of integers, which of the following is NOT necessarily the square of an
integer?
A. 9m
B. mn
C. m2
D. 9mn
E. 9m - 9n
25. Which of the following is a unit vector perpendicular to the vector
?
A.
B. (12,-5)
C.
D.
E.
26. If
and
A. 3t2 + 2t + 1
B. t2 - t + 1
C. t2 + 3t - 1
D. t2 + 3t + 3
E. (t2 + 3)/ (-1)
then which of the following could be
?
27. For values of
in the interval
the equation
, what is the total number of solutions for
in
?
A. 1
B. 2
C. 3
D. 4
E. No solutions
28. A small square is removed from a large square, reducing the area of the large square by 4%. How
many times longer is the side of the large square than the side of the small square?
A.
B.√5
C. 3
D. 5√2
E. 5
29. If
is defined as
must be true?
(I) x ↑ y = y ↑ x
(II) (x-1) ↑ (x+1) = (x ↑ x) - 1
(III) x ↑ (y+z) = (x ↑ y) + (x ↑ z)
A. I only
B. II only
C. III only
D. I and II only
, then for all numbers
which of the following
E. I, II, and III
30. If
, the expression
is equivalent to
A. 2(log x + log y)
B. 2(log x)(log y)
C. 2log x + log y
D. log2 + log x + log y
E. log x + 2log y
31. Given that
is a polynomial such that
,
, and
what is the value of
?
A. 0
B. 2
C. 3
D. 5
E. undefined
32. The average of 5 different integers is 33. The smallest of the 5 integers is 30. The largest of the five
integers is N. How many possible values of N are there?
A. 3
B. 6
C. 5
D. 4
E. 7
33. In the figure below, if
and the length of segment
perimeter of the triangle?
A. 26
B. 16
C. 24
D. 30
E. 32
34. Suppose that
A.
. What is the value of
3
√3
B. 3log28
C. 9log32
D. 6log32
E. 2log68
35. Find the value of
in the following equation
?
, what is the
A. 1
B. 2010
C. 2011
D. 2012
E. None of the above
36. Bob and Carol and Ted and Alice are backpacking in the wilderness. Each person carries x pounds of
equipment at the start of the trip. "Equipment" does not include food so the total weight of equipment
(4x) is constant. During the first night, Bob sneaks 10 pounds of equipment from his pack into Carol's.
Ted and Alice each sneak 7 pounds of equipment from their packs into Carol's. Later, when the other
three are picking berries, Carol divides all the equipment in her pack evenly amongst the packs of her
three pals. If Bob's pack now contains 54 pounds of equipment, how much did it contain originally?
A. 32 pounds
B. 35 pounds
C. 40 pounds
D. 42 pounds
E. 45 pounds
37. Let two 10x15 rectangles share a common corner and overlap. The distance from the bottom right
corner of one rectangle to the intersection point along the right edge of that rectangle is 9. What is the
approximate area of the shaded region?
A. 45
B. 58
C. 66
D. 86
E. 84
38. At a party, each person shakes hands with exactly 5 other people. There are a total of 60
handshakes. How many people are at the party?
A. 6
B. 12
C. 15
D. 24
E. 30
39. Write the inverse of the function
A. (x+3)/2
B. (1/2)x-3
C. -2x+3
D. 1/(2x-3)
as defined by
.
E. (x-3)/2